Learn about this topic in these articles:

Carolingian Empire

...of Verdun in 843 they agreed to divide the empire into three kingdoms. Francia Occidentalis in the west went to Charles II the Bald, Francia Orientalis in the east went to Louis II the German, and
Francia Media, including the Italian provinces and Rome, went to Lothar, who also inherited the title of emperor.

...sons of the Carolingian emperor Louis I (the Pious) divided the Frankish territory into three parts: Francia Occidentalis went to Charles II (the Bald), Francia Orientalis to Louis the German, and
Francia Media, the zone extending from the Low Countries to Italy, to the emperor Lothar I. This
Francia Media was partitioned by Lothar I in 855 between his sons: the elder of the two, Louis II,...

...the three brothers came to an agreement in the Treaty of Verdun (843). The empire was divided into three kingdoms arranged along a north-south axis: Francia Orientalis was given to Louis the German,
Francia Media to Lothar, and Francia Occidentalis to Charles the Bald. The three kings were equal among themselves. Lothar kept the imperial title, which had lost much of its universal character, and...